Segmental dies

ABSTRACT

A die nib is determined by a mathematically defined segmentshaped portion or die nib segment, a multiplicity of which are assembled together to form the die nib proper, each segment contacting its adjoining segment along a mathematically determined curvilinear transverse face whereby work stresses control the distribution of cohesive pressures along the interfaces of the segments, the segment-shaped portions having workpiece engaging walls forming a die opening of the shape desired for shaping the work material, the curvilinear transverse faces being illustrated by a wide variety of forms.

United States Patent [191 Freeman SEGMENTAL DIES [76] Inventor: Michael Walter Freeman, 401 David Whitny Bldg, Detroit, Mich. 48226 [22] Filed: Aug. 23, 1972 211 Appl. No.: 282,895

Related US. Application Data [63] Continuation of Ser. No. 722,778, April 19, 1968,

abandoned.

[52] US. Cl. 72/467 [51] Int. Cl. B2lc 3/04 [58] Field of Search 72/467; 425/461 [56] References Cited UNITED STATES PATENTS 1,922,110 8/1933 Schultz 72/469 2,578,229 12/1951 Clement et a1. 72/469 FOREIGN PATENTS OR APPLICATIONS 638,262 11/1936 Germany 72/468 [111 3,823,598 [451 July 16, 1974 Primary Examiner-Milton S. Mehr [5 7] ABSTRACT A die nib is determined by a mathematically defined segment-shaped portion or die nib segment, a multiplicity of which are assembled together to form the die nib proper, each segment contacting its adjoining segment along a mathematically determined curvilinear transverse face whereby work stresses control the distribution of cohesive pressures along the interfaces of the segments, the segment-shaped portions having workpiece engaging walls forming a die opening of the shape desired for shaping the work material, the curvilinear transverse faces being illustrated by a wide variety of forms.

9 Claims, 45 Drawing Figures PATENTEUJIIL 1 s 1914 mm am 23 H6. BB

FIG. IA

FIG.2A

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C CURVE OF EQUAL PRESSURE PRESSURE F l G. 5

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FIG. I4B

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1. A die nib comprising a plurality of segments fixed in position, said segments having mutually abutting surfaces, said surfaces intersecting a transverse plane in identical curvilinear lines, whereby each segment comprises one convex side surface and one concave side surface with a concave surface of one segment abutting a convex surface of an adjacent segment, said segments defining an inner opening of a desired shape, the configuration of said curvilinear lines determining a desired distribution of cohesive pressures resulting from working forces, each curvilinear line being defined by the equation r f( theta ), where r is a radial vector and f is a function of theta , where theta is the polar angle between a reference line passing through the center of said opening and the radial vector.
 2. A stationarY segmental die as set forth in claim 1, in which the cohesive pressures between segments increase over a determined initial range, 0 < or = theta < theta max, of the transversal faces of the segments, and in which the cross-sectional curves of the transversal faces, r f( theta ), satisfy in the above range the following inequality f( theta )+f''( theta )<0, and approximate, over a determined initial range, 0 < or = theta < theta max, the cross-sectional curves of the transversal faces given by the polar equation r f( theta ) K((1/k)n+ theta )1/n where K and n are positive constants satisfying the inequality K>(n2/n-1)1/2n.
 3. The stationary die nib of claim 1 wherein the equation r f( theta ) is equal to Sin ( theta )+ Alpha )/Sin Alpha and wherein the equation is a polar equation for a cross-sectional curve of the transversal face of each die nib and Alpha is the initial angle the tangent to the curve makes with the horizontal and is from above 0* to less than 90* and the maximum breadth of the effective portion of the die nib is determined from the expression Csc Alpha -1 and the cohesive pressure between segments is represented by the symbol P and is expressed by the formula P H/ Square Root (F''( theta ))2+(F( theta ))2 where H is a proportionality factor experimentally determined to establish cohesive pressure P, and the expression (f''( theta )2+(f( theta ))2 is a costant and wherein the cohesive pressure P between segments is equal along an effective portion of each completely abutting interface of the die nib segments and wherein each theta referred to above is the same as in r f( theta ) and is the polar angle between the horizontal line and the radial vector r.
 4. The stationary segmental die nib of claim 1 wherein the equation r f( theta ) is derived from the inequality of 2f''( theta )(f''''( theta )+f( theta ))>0 and wherein the equation is a polar equation for the cross-sectional curve of the transversal face of the segment and wherein the initial angle of the tangent of the curve makes with the horizontal is about from 0* to less than 90* and the maximum breadth of the effective portion of the die nib for logarithmic spirals is determined by eSCot Alpha-1 where S, a restricted theta , is the polar angle in radians the segmental curve sweeps through before ending at the periphery of the die nib and the cohesive pressure P between die nib segments is expressed by the formula P H/ Square Root (f''( theta ))2+( f( theta ))2 where H is a proportionality factor, the expression (f''( theta ))2+(f( theta ))2 is an increasing function of theta for an effective portion of the cross-sectional curve of the transversal face of the die nib segments.
 5. The stationary segmental die nib of claim 1 wherein r f( theta ) is the generic polar equation for the cross-sectional curve of the transversal face of the segment, the initial angle Alpha of the tangent of the curve makes with the horizontal is from above 0* to less than 90* and the maximum breadth Tmax, of the die nib is determined by the expression Tmax K( Square Root n-1/n)1/n-1 where K and n are independent constants satisfying the inequality K>(n2/n-1)1/2n and the cohesive pressure P between die segments is expressed by the formula P H/ Square Root (f''( theta ))2+(f( theta ))2 where H is a proportionality factor and the cohesive pressure between segments is increased over its effective portion a determined initial range of 0 < or = theta < theta max of the transversal segmental curves starting from the inner face of the die opening and (f''( theta ))2+(f( theta ))2 is a decreasing function of theta for 0 < or = theta < theta max.
 6. The stationary die nib of claim 4 wherein r f( theta ) is equal to e theta cot Alpha.
 7. The segmental die nib of claim 5 wherein r f( theta ) is equal to K((1/k)n+ theta )1/n where K and n are independent positive constants satisfying the inequality of K>(n2/n-1)1/2n.
 8. A die nib as claimed in claim 1, wherein said curvilinear lines extend in counterclockwise directions viewing from the top of said die nib.
 9. A stationary segmental die as set forth in claim 1, in which the cohesive pressure between segments, expressed by the formula: P H/ Square Root (f''( theta ))2+(f( theta ))2 where H is the factor of proportionality experimentally determined and r f( theta ) is the generic polar equation for the cross-sectional curve of the transversal face of the segment, is determined, in conjunction with operative conditions, by choice of the cross-sectional curves of the transversal faces of the segments from the group selected from: a. where the cohesive pressures between segments may be equal along the entire interface of the segments and (f''( theta ))2+(f( theta ))2 is a constant; b. where the cohesive pressures between segments may be greater toward the die opening than toward the periphery of the die nib and (f''( theta )2+(f( theta ))2 is an increasing function of theta ; c. where the cohesive pressures between segments may be made to increse over a determined initial range 0 < or = theta < theta max of the segmental curve starting from the inner face of the die opening and (f''( theta ))2+(f( theta ))2 is the decreasing function of theta for 0 < or = theta < theta max; d. where the cohesive pressures between segments may be further maximized at the inner face by reflecting the counter clockwise curves of (a), (b), and (c), and wherein Alpha is the initial angle the curve makes with the horizontal, as indicated in the below formula, having its chosen limits from above 0* to less than 90*; and the maximum breadth of the die nib wall Tmax for (a) is Csc Alpha-1; Tmax for logarithmic spirals in (b) is eSCot Alpha-1; and Tmax in (c) is ((n--S)/ Square Root n--1+1)1/n -1. 